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Let be a commutative ring with identity. The comaximal ideal graph of is a simple graph with its vertices are the proper ideals of R which are not contained in the Jacobson radical of , and two vertices and are adjacent if and only if . In this paper, a dominating set of is constructed using elements of the center when is a commutative Artinian ring. Also we prove that the domination number of is equal to the number of factors in the Artinian decomposition of . Also, we characterize all commutative Artinian rings(non local rings) with identity for which is planar.